Calculating instrument.



PATENTED DEC. 29

H. N. PIERCE. CALCULATING INSTRUMENT APPLIUATION FILED AUG. 28, 1902.

4 SHEETS-SHEET 1.

N0 MODEL.

WITNESSES.

H. N. PIERCE. CALCULATING INSTRUMENT.

APPLICATION FILED AUG. 28, 1902.

o MODEL.

PATBNTED DEC. 29, 1903.

4 SHEETS-SHEET 2.

A TTORNE YS.

PATENTED DEC. 29, 1903.

H, N. PIERCE. CALCULATING INSTRUMENT.

APPLICATION FILED AUG. 28, 1902.

4 SHEETS-SHEET 3.

N0 MODEL.

0:234 66 783 O|ll2|3Hl5 ABSCISSA SCALE.2]

ABS ISSA SCALE.

m WW7 A TTORNE Y8.

No. 748,566. PATENTED DEC. 29, 1903.

' H. N. PIERCE.

CALCULATING INSTRUMENT LPILIOAZIIOII FILED AUG. 23. 1902. 1T0 MODEL. 4 BHBETB-BHEBT 4.

' 2D 30 '40 O 60 IO 0 '0 ABSCISSA SCALE. ABSCI 36 4o SSA SCALE.

4854 SQ. 7A5,

ARf/I 40 ,ms,

SQ AHEA 57 50, m

ARM 0' sq, ms.

A fro/wk rs.

UNITED STATES vs l. ,5! "W 4'3 raienteu .necemner 29, 1960.

ll e. l? s:

HENRY NELSON PIERCE, 6F NEW Y.

CALCU LATING l l H To all whom it nttty concern.-

Beit known that I, HENRY NELSON PIERCE, a citizen of the Unit-ed States, and a resident of the city of New York, borough of Manhattan, in the county and State of New York, have invented a new and Improved Calculating Instrument, of which the following is a full, clear, and exact description.

My invention relates to an engineering instrument of precision reading direct by graphic method the cubic yards or cucic me tors in station lengths of railway read-beds, canals, and levees from simple data found in engineers field-notes of each cross-secticn namely, the sum of the side heights the center height.

Technically my invention relates to the determination of the volumes and functions of the volumes of such prismoidal solids having the full width of the road-bed throughout their length, and depends on the principle that any function of a prismoidal solid which can be expressed algebraically in terms of two variables may he represented bye "plane curve on a chart, which curve is determined by using these two variables as its coordinates. By this method I obtain first the end areas of prismoidal lengths (usually every hundred feet or every twenty meters) by a simple reading of the instrument, and by a second stage, using the two end areas thus found of any length, I obtain by the same method the volume of said lengths, also by a simple reading of the instrument, avoiding by the use of my invention the long calculations formerly necessary to arrive at such result.

Reference is to be had to the accompanying drawings, forming a part of this specification, in which similar characters of reference indicate corresponding parts in all the figures.

Figure 1 is a plan view of the obverse side of a worki ng chart and illustrates the manner of laying 01f abscissre by means of an offset radial bar and sliding needle, showing also by means of the bar in dotted position the manher of laying off ordinates and, finally, the reading of the chart in square yards. Fig. 1 is a plan view of the reverse side of the same chart, the manner of laying off ordinates, and the'reading in cubic yards. Fig. 2 is an edge view of the chart shown in Fig. l; and

(lilo model) 3 is a detril section through the chart, showingthe g in to" radialoar. Fig. t illustrates re-yard curve as it 6 .7. 8 mores t random cross-sec 'tional {twelve-fie t base, one-and-onehali lee'tz one Whose areas are determ by the thirty-square-yard curve, height abscissa; and sure.

of side ordinate.

c Fig. 10 illus trates the one-thou 'id-cubic-yard curve as it would appear established by ordinary recectans tilin l iilllifluizicurve the novel me ing volume curves up chart, which is by radial and .erential coordinates; and 12, 123, 1. illustrate random stations (one hundred. feet long, twelvefeet base, and-cne-hali one -foot slopes; Whose volumes are u ermined by the one thousand-enbio-yard curve, using one end. area as aoscissze and. the other end area as ordinate.

The chart A {shown in l) is in the form. of a sector and may be made of any suitable material. Said t upon its arc is prcvided with a scale B, re resenting' the suns of the side heights in feet, and at lower straight edge a scale C of center heights in feet, together with number of curved lines D, computed to predetermined numbers of square yards, which curved lines D are read in conjunction with the aforesaid scales, and while upon the drawings the lines D up to fifty square yards there are about one hundred lil'liy determined curves D on an actual chart. Fig. l illustrates reverse side of the chart, which has scales r1 d (1" and curves D similarly arranged, 1 to cubic yards when the two end areas of station are laid off on the two respective scales.

At the angle oi the straight edges of the chart A nut 10 is secured in the chart, as is shown conical pin. 11 is screwed in a pirotsup 'cotirdinates. Fig. ll. o-thcusand-cuhic-yard used in establish port for an ofEset radial bar or arm 12, which bar or arm at its pivot end is attached to 3 preferably weighted plate 13, having an attached conical thiuible 14 to fit over the pivot- Y an pin 11. This bar or arm is adapted to swing over the surface of the chart A and is pro vided between its ends with a clamp-slide 15, carrying a pin 16, to be adjusted to the scale C, and at the outer end of the radial bar 12 a shoe lZ is secured, which carries a needle 18, shaped to point to the divisions of the scale B. When the pin or pointer 16 points to the division on the scale representing a given. center height, the arm or bar 12 is swung over the scale B untilthe needle 18 points to the division on the scale B representing a given sum of the side heights. The pointer 16 will then be at the curve B, indicating the number of square yards-twenty, for example, as

shown in Fig. 1.. The reverse side works similarly, indicating cubic yards per station when end areas are laid off on the two scales-- seven hundred cubic yards, for example, as drown in Fig.

It will be observed that the radial bar 12 can be operated at either side of the chart, the pivotpin 11 for the bar maybe screwed into the nut from either side, and that the radial-bar 12 is capable of rotating in its inner and outer supports for the purpose of lifting the pointer 16 off the surface of the chart.

In the application of my invention to the determination of the cubic yards or cubic meters of station lengths the end areas or cross-sections can be expressed algebraically in terms of two variables-namely, the sum of the side heights and the center height, which information is to be found in the engineers data or field-netes of each crosseection, where the usual three stakes are set.

The following equation will clearly illustrate the manuerof determiningtheeud areas:

Letf +f equalsum of side heights in feet. Let j"equal center height in feet. Let

. 9" equal widthof road-bed in feet. Lets equal slope ratio. Then and area {gf/I fm) gjell (is! +fI/I) 2 and. area: 'rf

it follows that if a curve he laid down or established upon a plane surface by using 7 two such variables of any particular crosssectional area as its coordinates such a curve at every poiutreprescnts the area and is true for all possible variations of said two variables or coordinates, or, in other words, is true for all possiblevariations of form for end areas. For a graphic explication see gs. I to 9, inclusive,

llori co, to curve as rather Fig. l oi care-yard e as itineand by assuming successive arbitrary values forf in the second member of this last equation we obtain as many corresponding values forf +f, and using these successively-assunicd values off as ordinates on the chartv and laying oil their corresponding values of f'+-"" as abscissae we obtain a successionof points on the chart, and drawing a line. through all these points a thirty-square-yard curve is laid down upon the chart. The abscissa and ordinate scales are arbitrary, and a coarser or finer scale used in laying off the ordinates and abscissae only makes the chart larger or smaller. Other square-yard curves are laid down similarly, and the chart is thus constructed.

successively establishing similar curves upon the same plane surface at small intervals apart the one from the other and using as their respective coordinates the two variables that enter into the algebraic expression for cross-section areas successively larger or smaller a chart of determined curves is estahlished upon the plane surface of the chart, each curve representing the area of equal cross-sections whose respective variables have been used as the coordinates to establish that curvei My invention is then in a state for the findingof cross-section end areas,slnce any crosseectiou end area met with in practice is expressed in terms of its own two variables-- namely, the sum of the two side heights and the center height as given by the engineers data or field-notes at that particular cross section-and if these two variables are applied to the chart in the sense of two coon dinates the end of the ordinate must fall upon one or the determined curves of the chart or proportionately in the small distance between two consecutive curves, and the area of such particular cross-section is'directly read out, as-is indicated in Figs. 4, 5, 6, 7, 8., and 9.

The process is repeated for all the cross-sections of the line to be constructed.

Consideringthe volume ofastationslength, of which two and areas have now been found by the application of my invention without mathematical calculation,the volume of said station is found in cubic yards or onbio meters by a second stage of. the same procone, for the volume of a station can also be expressed algebraically in terms of two variables-namely, of its two end areas already ibuui-tbat is, a stations length whose volcute is, for example, one hundred cubic yards or one hundred cubic meters may have its upon another areas.

established upon this 5 small distance between consists in the :0 ratio. Then volume Z 2:

Svolume 3 -4800 Z T 88 2o ry@ +w-im) These two variables or end areas can therefore be used as coordinates to establish acurve plane surface, and this curve at every point will represent the volume of said stationslength (onehundred cubic yards or one hundred cubic meters) and be true for all possible variations in the size of the end For a graphic explication of the above see Figs. 10, 11, 12, 13, 14, and 15. The volume equation for constructing the volume curves is handled in exactly the same manner as is the area equation. Similar curves are successively established upon this plane surface at small intervals apart the one from the other, using as their coordinates the end areas of successively larger and smaller volumes, and a chart of determined curves is plane surface, each curve representing a volume Whose various possible end areas have been used as coordinates to establish that curve. Myinvention is then in a further state for the direct read- 5 ing of cubic yards or cubic meters of a stations length similarly as the aforementioned end areas are read, since the volume of any station met with in practice is expressed in terms of its own two variables or end areas,

50 and if the values of these two end areas in square units are applied to this chart in the sense of two coordinates the end of the ordinate must fall upon one of the determined curves of the chart or proportionately in the the two consecutive curves, and the volume of such particular station is readily read out, as is shown in the said Figs. 10 to 15, inclusive.

Briefly, my invention of a mechanical chart novel construction of the curves thereon, the arrangement of the scales w thereon, and the means for determining the leasi of the charts.

lliateria-Lly my invention consists in any thin substance having two plane surfaces in the form of the sector of a circle, preferably a quadrant, upon one side of which are simultaneously established a chart of the abovementioned area curves by coordinates and one circumferential scale for measuring ordinates and one straight radial scale for measuring abscissze, all with their-values in numerals and in any manner, as by printing,

lithographing or engraving, and filling in with colored wax, while on the reverse side are simultaneously established a chart of the above-mentioned volume curves by coordinates and one circumferential scale for measuring ordinates and one straight radial scale for measuring abscissse, all with their values in numerals in any manner, as mentioned with reference to the obverse side, the radial centers of both charts to be coincident save for the thickness of material.

Having thus described my invention, 1 claim as new and desire to secure by Letters Patent- 1. A calculating instrument consisting of a reversible chart in the form of a sector of a circle approximating a quadrant, on which are charted on the obverse side area curves by coordinates together with their respective ordinate and abscissa scales, all designated by numerals, while on the reverse side are chartered volume curves by coordinates together with their respective ordinate and abscissa scales, all designated by numerals, substantially as set forth.

2. A calculating instrument consisting of a reversible chart in the form of a sector of a circle approximating a quadrant, on which are chartered on the obverse side area curves by coordinates together with their respective ordinate and abscissa scales, all designated by numerals, while on the reverse side are chartered volume curves by coordinates togeiher with their respective ordinate and abscissa scales all designated by numerals, and a radial calculating-bar having pointers disposed with respect to the scales and area and volume curves whereby to determine graphically without mathematical calculation, the volume of stations, of railway road-beds or levees from the sum of the side heights and center height of the end cross-section areas, substantially as described.

3. A calculating instrument consisting of a reversible chart in the form of a sector of a circle, on which are charted on the obverse side area curves by coordinates, together with their respective ordinate and abscissa scales, all designated by numerals, while on the reverse side are charted volume curves by coordinates together with their respective ordinate and abscissa scales, all designated by numerals, an offset radial bar swinging to the center of the sector and over the chart interchangeable from one side to the other at will, a running clamp-slide on the said bar between its ends, a shoe at the free end of the bar, and pointing or indicating needles one of which is attached to the clamp-slide, and the other to the shoe, substantially as set forth.

4. Acalculating instrument consisting of a reversible chart in the form of a sector of a circle approximating a quadrant, on which the obverse side area curves their respective ordinate and abscissa scales, all designated by numerals, while on the reverse side are curves by coordinates toordinate and designated by numerals, an offset radial bar swinging to the center of the sector and over the chart interchangeable one side to the otherat will, a running clampbetween its ends, a shoe at the free end of the bar, pointing or indicating needles, one of which is attached to the other to the shoe, a reversible post constituting a pivot for the radial bar, a gyrating counterweighted support for the radial bar, and a thimble carried by the support to receive the said post, which the material radial center are charted on by coordinate together with charted volume gether with their respective abscissa scales, all

slide on the said bar the clamp-slide and post is located at of the chart, substantially as set forth.

5. A sector-chart,an offset radial bar swingsector and over the obverse or reverse side at with and carryinga runshoe at the outer end of ing about the center of the the chart on will, in combination ning clamp-slide, a said bar, pointing and indicating needles attached one to the running clamp-slide and the other to the shoe, an inner central carrying support for the bar counterweighted to induce even wear, a thimble carried by said carrying-support, and a pivot-point reversibly attached to the chart to receive the said thimble, the attachment of the pivot-point being at the material radial center of the chart, substantially as set forth.

6. In a calculating instrument, having charts on the obverse and reverse sides thereof, an offset radial bar, offset, but always parallel to the radii of the charts on the obverse or reverse side of the instrument, an indicatlug-needle carried by the radial bar, said needle always being on a true radius of the chart, substantially as set forth.

7. In a calculating instiument, an offset radial bar revolving in its supports and raised from the surface of the chart, and a needlewith the radial bar, which needle-point, by reason of the offset and raised position of the radial bar is slightly lifted from the surface of the chart, when the bar is partially rotated and swung over the chart.

8. A calculating instrument having one of its faces marked to indicate cubic yards, the reverse face being marked to indicate square yards, and pivoted indicating means reversibly mounted whereby to be moved over either of said faces, substantially as set forth.

9. A calculating instrument having one of its faces marked with a series of curves designating cubic yards, the reverse side of said instrument having a series of nating square yards, and a reversible radial pointer adapted to be moved over the aforesaid faces.

lO. A calculating instrument comprising a chart having marked thereon area curves by coordinates together with their respective ordinate and abscissa scales, all designated by numerals, and indicating means swingable over said chart in an arc, the line of which intersects said area scales, all designated by numerals, and indicating means adapted to move over said chart in a line which intersects the aforesaid curves, substantially as set forth.

12. A calculating instrument eomprisinga reversible chart in over either of said charted faces.

13. A calculating instrument comprising a reversible chart in the form of a sector of a circle approximating the quadrant, the obverse and reverse sides thereof being relatively differentially charted with a graduated series of curved lines of measurement, and a reversible radial indicating-bar movable over the charted faces, substantially as set forth.

14. A calculating instrument having one of its faces marked with relatively differentially HEN RY NELSON PIERCE.

Witnesses:

J. FRED. AoKER, JNo. M. BITTER. 

